Subgroups — #66923

Order 352.

56 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄²×C₁₁	C₂	1	1	yes	maximal, characteristic
2	C₄⋊Dic₁₁	C₂	1	2	yes	maximal
3	Dic₁₁⋊C₄	C₂	1	4	yes	maximal
4	C₂×C₄×C₁₁	C₂²	1	2	yes	—
5	C₂×C₄×C₁₁	C₂²	1	1	yes	characteristic
6	C₂×Dic₁₁	C₂²	1	4	yes	—
7	C₂²×C₁₁	C₂³	1	1	yes	characteristic
8	C₄×C₁₁	—	2	2	no	—
9	C₄×C₁₁	Q₈	1	2	yes	—
10	Dic₁₁	—	2	4	no	—
11	#125	—	11	1	no	maximal, Sylow
12	C₂×C₁₁	C₂×Q₈	1	1	yes	characteristic
13	C₂×C₁₁	#41	1	2	yes	—
14	C₄⋊C₄	—	11	4	no	—
15	C₄⋊C₄	—	11	2	no	—
16	C₄²	D₁₁	1	1	yes	characteristic
17	C₁₁	#125	1	1	yes	characteristic, complemented, Sylow
18	C₂×C₄	—	11	4	no	—
19	C₂×C₄	C₂×D₁₁	1	2	yes	—
20	C₂×C₄	C₂×D₁₁	1	1	yes	characteristic
21	C₂²	C₂²×D₁₁	1	1	yes	characteristic
22	C₄	—	2	2	no	—
23	C₄	—	22	4	no	—
24	C₄	Dic₂₂	1	2	yes	—
25	C₂	C₂×Dic₂₂	1	1	yes	characteristic
26	C₂	#4339	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂²	C₂²×D₁₁
commutator, socle, prime radical, cosocle	C₂²×C₁₁	C₂³
Fitting	C₄²×C₁₁	C₂
hypercenter	C₄²	D₁₁
hypocenter	C₁₁	#125
LCS	G ▷ C₂²×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂² ◁ C₄²

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
17. C₁₁	#125	semidirect

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.